There exists a variety of experiments involving human subjects in which one desires to compare two or more populations relative to a measurement Y where Y depends on some variables X1,...,Xk, k greater than 1 and where the value of Xi for each i cannot be controlled but yet is restricted to a finite interval. In such experiments it is not possible to erase the effect of Xi's by randomization. One such example is where one population consists of healthy controls and the other consists of subjects which have some disease. Thus, the main objective of this research is to develop procedures for comparing two or more populations relative to a measurement Y where Y depends on variables Xl,...,Xk, k greater than 1. These comparisons will be formulated in a hypothesis testing framework. Both parametric and distribution-free solutions will be sought. The basic approach in both the parametric and distribution-free solutions will be to use regression techniques to find a suitable relationship between Y and X1,...,Xk and then make use of this relationship in constructing a test for the particular hypothesis of interest. It will probably be necessary to use numerical integration as well as monte carlo techniques in order to investigate properties of these tests. A second portion of the research consists of developing nonparametric methods for determining if E(Y(t)), a lesser than t lesser than b for one population lies above the same function for another population for all a lesser than t lesser than b where E(Y(t)) is a continuous function. The data in this problem consists of the curves Y(t), a lesser than t lesser than b.